Question

1. A sample of n = 64 adults was taken, and researchers collected data on their salary per day in dollars.

1. A 95% confidence interval for µ is (140.7, 159.3). Interpret the confidence interval.
   1. There is a 95% chance that µ is in (140.7, 159.3).
   2. There is a 95% probability that µ is in (140.7, 159.3).
   3. I am 95% confident that µ is captured in the interval (140.7, 159.3).
   4. All of the above.

2. Given the sample data and confidence interval in a., do you think that the true average salary per day of adults, µ, is below 160?

1. Yes, the confidence interval is entirely below 160.
2. Unsure, the confidence interval does not contain 160.

Answer 1

Solution :

a) All of the above

In the interpretation about the 95% confidence interval for there is all statements are correct. we say that 95% chance that the mean is lies between the (140.7, 159.3). Also 0.95 probability outoff 1 mean is lies in between (140.7,159.3) Also mean is captured between (140.7,159.3) so all the statments about the interpretation of confidence interval is true.

b) Yes , the confidence interval is entirely below.

In the example a) there is 95% confidence of the average of the sample data is lies in the interval (140.7 , 159.3)

so we say that 95% sample true average salay per day of adults ,sample mean is below 160. because upper limit of confidence interval is 159.3 which is less than 160.